{
  "id": "1005.1272",
  "version": "v1",
  "published": "2010-05-07T18:32:22.000Z",
  "updated": "2010-05-07T18:32:22.000Z",
  "title": "Adjoint representation of E_8 and del Pezzo surfaces of degree 1",
  "authors": [
    "Vera V. Serganova",
    "Alexei N. Skorobogatov"
  ],
  "comment": "21 pages",
  "categories": [
    "math.AG"
  ],
  "abstract": "Let X be a del Pezzo surface of degree 1, and let G be the simple Lie group of type E_8. We construct a locally closed embedding of a universal torsor over X into the G-orbit of the highest weight vector of the adjoint representation. This embedding is equivariant with respect to the action of the Neron-Severi torus T of X identified with a maximal torus of G extended by the group of scalars. The T-invariant hyperplane sections of the torsor defined by the roots of G are inverse images of the 240 exceptional curves on X. This extends the main result of our previous work to del Pezzo surfaces of degree 1.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-05-07T18:32:22.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14J26",
      "22E46"
    ],
    "keywords": [
      "del pezzo surface",
      "adjoint representation",
      "highest weight vector",
      "simple lie group",
      "t-invariant hyperplane sections"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1005.1272S"
    }
  }
}